Theory of Crystallization under Equilibrium Polymerization in a Solution and the Investigation of its Melting Properties

We generalize a recently investigated lattice model of semiflexible polymers formed under equilibrium polymerization in a solution and conduct a comprehensive investigation of its melting properties. The model is characterized by six energies, three of which are for the interaction between the middle-group, the end-group and the solvent, and the remaining three represent energies for a gauche bond, a hairpin turn and a pair of neighboring parallel bonds. A polymer has two end-groups and at least one chemical bond. Two activities control the end-group and the middle-group densities, respectively, and give rise to polydisperse chains whose number is not fixed. We study the melting properties with various model parameters under conditions of fixed pressure, and compare our results with experimental data on fixed length and polydisperse polymers, whenever available. We investigate the effect of monomer interactions, nature of end-groups, chain rigidity, solvent quality, degree of polymerization, etc on the melting properties such as the melting temperature, latent heat, and energy and entropy of fusion. Our theory is thermodynamically consistent in the entire parameter space and improves upon the classical theories; hence our results should prove useful.